When combining an already enchanted pickaxe with a cursed pickaxe the repaired pickaxe remains enchanted

When combining a pickaxe with a curse on it, such as Curse of Vanishing, or Curse of Binding, in the crafting grid, the resulting pickaxe acts as though it is still enchanted with the original enchantments, such as Silk Touch or Fortune. But the text normally showing the enchantments of the tool only shows the curse.

In short, if an enchanted Pickaxe is combined with a cursed pickaxe in the crafting grid, it will act as though it was combined in an anvil, with the only difference being the enchantments are not visible.

 

I would advise looking into this as there is a potential that these items can be combined in an anvil with other enchantments to make an infinitely powerful item.